Patel arrives at No 10 carrying a copy of the Sun in her bag. Photograph: Will Oliver/EPA

Speaking on BBC Radio 4’s Today programme, Patel, who has been prominent in the leave campaign, said: “There would be more than enough money to ensure that those who now get funding from the EU including universities, scientists, farmers, regional funds, would continue to get money.”

Pressed on how Britain would spend the £160m a week it currently contributes to the EU, Patel confirmed that a post-Brexit government would spend £100m a week on the NHS. But she was vague about the remaining £60m, saying only that it would go towards cutting VAT on fuel.

Asked how much would be spent on schools, new roads and tax cuts, Patel said: “We have not said we would spend money on those items. We have said that we would spend British taxpayers’ money on a range of priorities including the NHS and in particularly as well on [cutting] VAT on fuel. So those are the two areas that we have said we will spend that money on.”

Asked to clarify other spending promises, she said: “When we take back control of the money that we currently send to the European Union, the government of the day will have options and choices as to how they chose to spend that money.”

Alan Johnson, the Labour former home secretary and remain campaigner, said the economy would take such a big hit if Britain left the EU that it would more than wipe out its contribution.

He said: “Vote Leave say, in their latest fantasy economics, ‘we are going to give all this money back’. That money would not exist. GDP only has to be hit by just over half a per cent to eradicate the £8bn that is sent to Europe and distributed through farming subsidies etc. Losing our access to the biggest commercial market in the world … is going to damage our economy.”

Johnson said staying in the EU would help control illegal immigration, free movement and immigration from outside the EU. He told the BBC: “Of those free movement gives us the benefit of the single market.

“Remaining part of the single market helps us control the other two forms of immigration. If we leave the situation is going to be worse. We won’t be protected by the Dublin accord. If anyone believes that our UK border in Calais is going to survive us leaving the EU, then once again they are in the realms of fantasy.”

Johnson admitted he was anxious about the vote. He said: “I was always going to get nervous at this stage of the game. There was no time at all during this campaign, when you would have found me thinking this was going to be a walk in the park or being complacent. Every vote counts. Getting closer to the date is obviously a time when the intensity increases.”